3 solutions

Solution 1

Instead of Convert (bad word, in this case!), use Decimal.TryParse or Decimal.Parse. It won't improve your code much, but TryParse will help you to avoid exception (but there is nothing wrong with exceptions). More importantly, you will understand better what you are doing. You are parsing, not "converting". And the parse may or may not be successful, depending on input.

As the data comes from UI when a used types invalid text, it is unavoidable in most cases. You need to handle such situations.

First of all, I'm glad that it's from UI, so you are not doing fundamentally wrong thing. Good.
(Sorry, I could see it's from UI from your code sample, did not pay attention. I'll remove redundant advice from my answer.)

Now, what did you do? Executed under the debugger? What is the input string? the problem is very simple.
Also, do you have exception handling on top of UI cycle. This is done in a special way available in the UI library, so what is that (Forms, WPF, something else?)
—SA

It may help, but not in all cases. Sometimes this is absolutely useless. It depends on required range. With a small range, NumericUpDown works very well:
http://msdn.microsoft.com/en-us/library/57dy4d56.aspx.

Well, as I said, it may help, not in all cases. It can work in case where all the values which fit in the pattern fit in the range, which is likely in case of decimal. But you cannot express the constraint to the range such as 0 .. 1234561233435...
—SA

You are welcome. Will you accept it formally (green button)? I strongly recommend you to use this exception handling in all cases, even if you do other exception handling in application or even in the same thread but deeper in stack. This is a top level of exception stack in the UI, will catch everything. If you don't to it, you cannot guarantee that your application continues to execute.

(By the way, you never mentioned that you were using comma-separated input, even when you were asked for detail. That's the problem.)
—SA

My 5... Where did you get this comma, how did you guess..? OP never mentioned that, even when asked for detail.
By the way, I added another answer, to properly catch all UI thread exceptions, an important technique to use in all cases.
—SA